Problem: Rewrite as a simplified fraction. ${0.\overline{71} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 71.7171...\\ 1x &= 0.7171...\end{align*}}$ Subtracting the two equations, we have: ${99x = 71}$ ${x = \dfrac{71}{99}} $